Question: The equation of a circle $C$ is $x^2+y^2+14x+18y+126 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2+14x) + (y^2+18y) = -126$ $(x^2+14x+49) + (y^2+18y+81) = -126 + 49 + 81$ $(x+7)^{2} + (y+9)^{2} = 4 = 2^2$ Thus, $(h, k) = (-7, -9)$ and $r = 2$.